What is the gear ratio?

• A. Driver Gear Pitch Diameter Divided by Driven Gear Pitch Diameter
• B. Sum of Pitch Diameters
• C. Difference of Pitch Diameters
• D. Driven Gear Pitch Diameter Divided by Driver Gear Pitch Diameter

Answer: (D)

Gears transmit motion through their pitch circles, not the outer edges, so the gear ratio is determined by how fast each gear would rotate if they were meshing and keeping the same contact speed at the pitch circles. The tangential (pitch-line) velocity must be the same on both gears, which gives the relationship ω_driver × D_driver = ω_driven × D_driven. If you define the gear ratio as the input speed divided by the output speed, then the gear ratio equals the driven pitch diameter divided by the driver pitch diameter. In other words, i = D_driven / D_driver. This means a larger driven gear compared to the driver will produce a gear ratio greater than one, so the driver must rotate more times to make the driven rotate once. The other expressions (sums, differences, or the inverse of this ratio) don’t reflect the way the pitch circles constrain motion and set the correct speed relationship.